from time import clock
import matplotlib.pyplot as plt
import scipy
from qutip import *
from qutip.piqs import *
from scipy.sparse import load_npz, save_npz
N = 20
ntls = N
nds = num_dicke_states(N)
print("The number of Dicke states is", nds)
[jx, jy, jz] = jspin(N)
jp = jspin(N, "+")
jm = jspin(N, "-")
system = Dicke(N = N)
###The number of Dicke states is 121
a = 1/np.sqrt(2)
b = 1/np.sqrt(2)
css_symmetric = css(N, a, b)
css_antisymmetric = css(N, a,-b)
excited_ = dicke(N, N/2,N/2)
superradiant = dicke(N,N/2,0)
subradiant = dicke(N,j_min(N),-j_min(N))
ground_ = dicke(N,N/2,-N/2)
ghz_ = ghz(N)
# here we set the initial coefficients
gE = 0 # local emission
gD = 0 # local dephasing
gP = 0 # local pumping
gCE = 1 # collective emission
gCD = 0 # collective dephasing
gCP = 0 # collective pumping
w0 = 1 # bare frequency
wi = 0 # coherent drive frequency
# spin hamiltonian
h0 = w0 * jz
hint = wi * jx
h = h0 #+ hint
#set initial conditions for spins by initializing the system and building the Liouvillian matrix
system = Dicke(hamiltonian = h,
N = N,
emission = gE,
pumping = gP,
dephasing = gD,
collective_emission = gCE,
collective_pumping = gCP,
collective_dephasing = gCD)
clock_t0 = clock()
lind = system.lindbladian()
liouv = system.liouvillian()
clock_tf = clock()
dt_clock = clock_tf - clock_t0
print("Time (in seconds) to generate the Liouvillian for N = 20 TLSs:", dt_clock)
###Time (in seconds) to generate the Liouvillian for N = 20 TLSs: 0.05499199999999993
## Solution of the dynamics for different initial conditions
# parameters for the time integration of the dynamics
nt = 1001
td0 = np.log(N)/(N*gCE) # delay time is used as a reference
tmax = 10 * td0
t = np.linspace(0, tmax, nt)
# initial states
rho01 = excited_
rho02 = superradiant
rho03 = css_symmetric
rho04 = css_antisymmetric
rho05 = subradiant
rho06 = ghz_
#Excited
clock_t0 = clock()
result1 = mesolve(liouv, rho01, t, [], e_ops = [jz, jp*jm, jz**2],
options = Options(store_states=True))
rhot1 = result1.states
jz_t1 = result1.expect[0]
jpjm_t1 = result1.expect[1]
jz2_t1 = result1.expect[2]
clock_tf = clock()
dt_clock = clock_tf - clock_t0
print("Elapsed time (in seconds) for this run: ", dt_clock)
#Superradiant
clock_t0 = clock()
result2 = mesolve(liouv, rho02, t, [], e_ops = [jz, jp*jm, jz**2],
options = Options(store_states=True))
rhot2 = result2.states
jz_t2 = result2.expect[0]
jpjm_t2 = result2.expect[1]
jz2_t2 = result2.expect[2]
clock_tf = clock()
dt_clock = clock_tf - clock_t0
print("Elapsed time (in seconds) for this run: ", dt_clock)
#CSS Symmetric
clock_t0 = clock()
result3 = mesolve(liouv, rho03, t, [], e_ops = [jz, jp*jm, jz**2],
options = Options(store_states=True))
rhot3 = result3.states
jz_t3 = result3.expect[0]
jpjm_t3 = result3.expect[1]
jz2_t3 = result3.expect[2]
clock_tf = clock()
dt_clock = clock_tf - clock_t0
print("Elapsed time (in seconds) for this run: ", dt_clock)
#CSS Antisymmetric
clock_t0 = clock()
result4 = mesolve(liouv, rho04, t, [], e_ops = [jz, jp*jm, jz**2],
options = Options(store_states=True))
rhot4 = result4.states
jz_t4 = result4.expect[0]
jpjm_t4 = result4.expect[1]
jz2_t4 = result4.expect[2]
clock_tf = clock()
dt_clock = clock_tf - clock_t0
print("Elapsed time (in seconds) for this run: ", dt_clock)
#Subradiant
clock_t0 = clock()
result5 = mesolve(liouv, rho05, t, [], e_ops = [jz, jp*jm, jz**2],
options = Options(store_states=True))
rhot5 = result5.states
jz_t5 = result5.expect[0]
jpjm_t5 = result5.expect[1]
jz2_t5 = result5.expect[2]
clock_tf = clock()
dt_clock = clock_tf - clock_t0
print("Elapsed time (in seconds) for this run: ", dt_clock)
#GHZ
clock_t0 = clock()
result6 = mesolve(liouv, rho06, t, [], e_ops = [jz, jp*jm, jz**2],
options = Options(store_states=True))
rhot6 = result6.states
jz_t6 = result6.expect[0]
jpjm_t6 = result6.expect[1]
jz2_t6 = result6.expect[2]
clock_tf = clock()
dt_clock = clock_tf - clock_t0
print("Elapsed time (in seconds) for this run: ", dt_clock)
###
##Elapsed time (in seconds) for this run: 1.4128720000000001
##Elapsed time (in seconds) for this run: 1.3064499999999994
##Elapsed time (in seconds) for this run: 1.2567909999999998
##Elapsed time (in seconds) for this run: 1.333939
##Elapsed time (in seconds) for this run: 0.5167439999999992
##Elapsed time (in seconds) for this run: 1.3920459999999997
#####Visualization
jmax = (0.5 * N)
j2max = (0.5 * N + 1) * (0.5 * N)
label_size = 20
label_size2 = 20
label_size3 = 20
label_size4 = 15
plt.rc('text', usetex = True)
fig1 = plt.figure()
plt.plot(t/td0, jz_t1/jmax, '-.', label = r"$|\frac{N}{2},\frac{N}{2}\rangle$")
plt.plot(t/td0, jz_t2/jmax, '-', label = r"$|\frac{N}{2},0\rangle$")
plt.plot(t/td0, jz_t3/jmax, '-', label = r"$|+\rangle_\mathrm{CSS}$")
plt.plot(t/td0, jz_t4/jmax, '-', label = r"$|-\rangle_\mathrm{CSS}$")
plt.plot(t/td0,jz_t5/jmax, '-', label = r"$|0,0\rangle$")
plt.plot(t/td0,jz_t6/jmax, '--', label = r"$|\mathrm{GHZ}\rangle$")
#plt.ylim([-1,1])
plt.xlabel(r'$t/t_\mathrm{D}$', fontsize = label_size3)
plt.ylabel(r'$\langle J_{z} \rangle(t)$', fontsize = label_size3)
plt.xticks([0,(tmax/2)/td0,tmax/td0])
plt.yticks([-1,0,1])
plt.legend(fontsize = label_size4, ncol = 2)
# plot
plt.title(r'Total Inversion', fontsize = label_size3)
plt.show()
plt.close()
fig2 = plt.figure()
plt.plot(t/td0, jpjm_t1/j2max, '-.', label = r"$|\frac{N}{2},\frac{N}{2}\rangle$")
plt.plot(t/td0, jpjm_t2/j2max, '-', label = r"$|\frac{N}{2},0\rangle$")
plt.plot(t/td0, jpjm_t3/j2max, '-', label = r"$|+\rangle_\mathrm{CSS}$", linewidth = 2)
plt.plot(t/td0, jpjm_t4/j2max, '-', label = r"$|-\rangle_\mathrm{CSS}$")
plt.plot(t/td0,jpjm_t5/j2max, '-', label = r"$|0,0\rangle$")
plt.plot(t/td0,jpjm_t6/j2max, '--', label = r"$|\mathrm{GHZ}\rangle$")
#plt.ylim([0,1])
plt.xticks([0,(tmax/2)/td0,tmax/td0])
plt.yticks([0,0.5,1])
plt.xlabel(r'$t/t_\mathrm{D}$', fontsize = label_size3)
plt.ylabel(r'$\langle J_{+}J_{-}\rangle(t)$', fontsize = label_size3)
plt.legend(fontsize = label_size4, ncol = 2)
# plot
plt.title(r'Light Emission', fontsize = label_size3)
plt.show()
plt.close()
fig3 = plt.figure()
djz1 = (jz2_t1- jz_t1**2)/jmax**2
djz2 = (jz2_t2- jz_t2**2)/jmax**2
djz3 = (jz2_t3- jz_t3**2)/jmax**2
djz4 = (jz2_t4- jz_t4**2)/jmax**2
djz5 = (jz2_t5- jz_t5**2)/jmax**2
djz6 = (jz2_t6- jz_t6**2)/jmax**2
plt.plot(t/td0, djz1, '-.', label = r"$|\frac{N}{2},\frac{N}{2}\rangle$")
plt.plot(t/td0, djz2, '-', label = r"$|\frac{N}{2},0\rangle$")
plt.plot(t/td0, djz3, '-', label = r"$|+\rangle_\mathrm{CSS}$")
plt.plot(t/td0, djz4, '-', label = r"$|-\rangle_\mathrm{CSS}$")
plt.plot(t/td0, djz5, '-', label = r"$|0,0\rangle$")
plt.plot(t/td0, djz6, '--', label = r"$|\mathrm{GHZ}\rangle$")
#plt.ylim([-1,1])
plt.xticks([0,(tmax/2)/td0,tmax/td0])
plt.yticks([0,0.5,1])
plt.xlabel(r'$t/t_\mathrm{D}$', fontsize = label_size3)
plt.ylabel(r'$\Delta J_{z}^2(t)$', fontsize = label_size3)
plt.rc('xtick', labelsize=label_size)
plt.rc('ytick', labelsize=label_size)
plt.legend(fontsize = label_size4, ncol = 2)
plt.title(r'Second-moment Collective Correlations', fontsize = label_size3)
plt.show()
plt.close()
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